ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   162.   71.0 Blue      
 2     2   171.   83.3 Brown     
 3     3   178.   76.4 Grey      
 4     4   170.   67.9 Brown     
 5     5   170.   79.8 Blue      
 6     6   167.   85.4 Grey      
 7     7   174.   67.1 Grey      
 8     8   170.   79.1 Blue      
 9     9   175.   85.4 Green     
10    10   165.   76.2 Grey      
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1] -0.846476107  0.182897408 -0.708383983 -1.679437651 -0.703403624
   [6] -0.423046138 -0.501975867  0.623751651  1.954210474  0.386136181
  [11] -0.713706628 -0.622758538  1.044480143 -1.815385454  0.893312622
  [16]  0.018021664  1.496004487  1.745083543 -0.404119884 -0.165147251
  [21]  1.171065143  0.701378013  0.097304882  0.141591386  0.082401605
  [26]  0.083527479  0.704082209 -0.182533175 -1.676873471  1.000719873
  [31]  1.401965028 -0.102221320  0.693226091 -0.345550925 -0.356444270
  [36] -1.027811306 -0.411588336  0.521354454 -0.691289923  1.855059493
  [41]  0.651679022 -0.509024948 -0.994572579 -0.674144943  0.967443942
  [46]  1.117319701  1.059319661 -0.297643935  0.112856629  0.824292376
  [51]  1.693337402 -1.592521440 -0.069199604 -0.857190291  1.593343480
  [56]  0.124055144  1.020463537  0.953628318 -1.629044175  0.051679589
  [61] -0.052705111 -0.560392347 -1.638908125 -0.463141342 -1.168378184
  [66] -1.080363576  0.125483825 -1.423702434 -1.196049867  0.922289476
  [71] -0.718702957 -0.721780874 -0.731272352 -1.413721826  0.077566124
  [76] -1.045552125  0.306168064 -0.177066563 -0.089639537  1.283774866
  [81]  0.035664778  0.214906763  0.093766861 -0.251757947 -0.288781592
  [86]  0.160611450 -0.424415393  0.786573126  0.937327534 -1.996806620
  [91] -0.880119180  1.994439349  0.317962665 -0.924875632  0.319766565
  [96] -0.248280114  3.059390836 -0.824748053 -2.128856146  0.539296977
 [101]  0.497986133 -0.838510436  1.042951570 -0.718119208  1.366554988
 [106] -0.228415538 -0.054090851 -1.271944926  0.360619254 -3.261171698
 [111]  1.260181022 -1.281143103  1.183307036  0.159561699 -1.479444197
 [116]  0.861395150 -2.054299185 -0.114020222  0.316927530 -1.097231628
 [121] -0.328647434 -1.240188876 -1.096128308 -1.019893716 -0.069134388
 [126]  0.773879845 -0.116268048  2.537809672  1.220817424 -1.502719662
 [131]  2.062852452 -1.211718035  0.412666317 -1.478936525  3.753102279
 [136] -0.165884980  0.522123860 -0.071466880 -0.343312401  0.893195129
 [141]  0.679336861  0.328482012 -0.653897651  0.347608507  0.268566347
 [146]  2.025395321 -1.017366109 -0.214983155  0.417472529  0.482512514
 [151] -0.898767270  0.501489818 -0.929235737  1.871865456 -0.037691568
 [156] -0.294346244  0.146587386  0.380627043  1.669201232 -1.562824243
 [161] -0.950831330 -1.274374682 -0.690797669  0.453289244 -1.291824446
 [166] -1.127992811 -0.790492004 -0.427591336  0.006034587 -0.189562948
 [171]  0.125465299  0.918971580  2.273110597 -0.360296603  0.390718835
 [176] -2.226005987  2.193188993  0.131590443 -1.587439638 -1.607827321
 [181] -1.029941337 -1.703361302 -0.160417207  0.309783569  0.193219567
 [186] -1.690236774  0.703353779 -0.090924244  0.014486564  0.278200868
 [191]  2.010630344 -0.661667792 -0.432036789 -0.973671240  0.957775435
 [196] -0.012243238  1.739510483  0.948016656 -0.448607501 -0.304266918
 [201]  1.443775142 -1.595461818  1.395252200  1.909224098 -0.028044766
 [206]  0.200141036  0.894798062  1.096448946  0.119783321  0.485669612
 [211]  1.691443193  1.516585260 -0.591029422 -0.190944769 -0.778725308
 [216] -0.774091577  1.154522068  0.746508233  1.737871842 -0.449513181
 [221]  1.132940757 -0.953847283 -0.445587211 -1.336141139 -0.602997118
 [226]  0.363361658  1.101063917 -1.249421922 -0.022977105  1.222765323
 [231]  1.006235193 -0.661515533 -0.632103835  0.311607516 -1.369473775
 [236]  0.989391044  0.525715461 -0.141948469 -1.138927709  0.163824675
 [241] -2.020066094  2.466948199  1.380535967 -2.105537283 -0.278722398
 [246] -1.919800185  1.411701984  0.528232173  0.181899122  0.453277208
 [251]  0.743801916 -0.384843651  1.941676417 -1.015613390 -0.079275856
 [256]  0.472494716 -0.841674108  2.158093166  1.087489809 -0.144945795
 [261]  1.479581749  1.776884457  0.604253952 -2.685715718 -0.811964991
 [266]  0.174748952  0.355912403 -1.659149046  1.926220118 -1.039143280
 [271] -0.826744934 -0.369156641  0.340685964  0.894946424  1.078446332
 [276] -0.400826463  1.522383105  0.114050784  2.245451827 -1.904449876
 [281]  1.365507926  1.006283999 -1.486618092 -1.393005059  0.466193198
 [286] -1.235869990  0.709972839  1.119287983 -0.080204714 -0.018823470
 [291] -1.163683235  0.271710795  0.593701786 -1.404317095  0.683732163
 [296] -1.727120736  0.166338661  0.464853934 -0.783349607 -0.113537952
 [301]  0.868796771 -1.305716826 -1.053532674  0.571947222 -1.301242256
 [306]  1.986534958  0.204214164  0.177951927 -0.364876179 -0.540200714
 [311] -0.784961925 -0.167585323 -1.255304731  0.873100215  0.069844704
 [316]  1.244437283 -0.963693823  0.219649275 -0.408617915 -0.793180996
 [321]  0.292544159  0.222422712 -1.148637446 -1.314315950  1.570640907
 [326] -2.096693716  1.186643134 -1.372004899 -0.895111403 -1.232252205
 [331]  0.744417695  0.879622384 -0.377670076  1.033148651 -0.803733059
 [336] -0.057989247 -0.703766855  0.215217393  0.006079127  0.883543260
 [341] -0.304918741 -1.266296021  1.619495004  1.071931399 -0.193463735
 [346]  0.783142746  0.425317391 -0.532606211 -0.313268105 -0.493124490
 [351] -1.077339468  1.627365437  0.645834737  0.620401680 -0.347648078
 [356]  0.918405115 -0.091526318  0.392755127  1.076384538  0.812672350
 [361]  0.898315338  0.288559308 -0.569768916 -0.020769358 -0.455734087
 [366]  1.430925278 -1.313357802 -1.347976179  0.248474616 -1.218601497
 [371]  1.301027177 -0.990610254 -0.622483779  0.661998476 -1.191435520
 [376]  2.010873734 -0.949128237 -1.463970288  0.195724393  1.057867969
 [381]  0.648857356  1.063077446  0.273800182  1.946204265  0.223363798
 [386] -0.438631977  0.099713888  0.306218409  0.223167587  0.171227811
 [391] -0.960646392 -0.793219259 -0.427901020 -0.548751305 -0.508300513
 [396] -0.570586651 -1.050283522  1.027673786  0.692915431  1.608692882
 [401]  0.299116619  0.977385900 -1.750447638 -0.419016156  0.616318048
 [406] -1.531131915  0.968157503 -0.319230473 -0.487957157 -0.699380894
 [411] -0.534422401 -0.301351303  0.095374791 -0.365482482  0.496532807
 [416]  0.212071538  1.090193082  0.889503321 -1.530678647  1.343187570
 [421]  0.701463439 -0.889459034 -1.219027224 -0.717686990  0.867588143
 [426] -1.991314006 -0.223642864  0.077615924 -0.621128905  0.975544104
 [431]  0.609142075 -2.056473839 -0.105534814  1.547511309 -2.172846776
 [436] -0.222275175  0.032946474  0.505473557  2.389420124 -0.153788045
 [441]  0.205887894 -1.252650106  0.280569689  0.552466653 -1.663347174
 [446] -0.671893950 -0.550510744  0.290450013  0.816483055  0.313739809
 [451]  0.477326572 -0.368324654 -0.052987214 -0.220098031 -0.111193138
 [456] -1.923141509 -1.097312891  1.194329180  0.865721078  1.437486704
 [461] -1.053951922 -0.753713288 -0.987510766  0.056266393  0.408271814
 [466]  0.657828408 -1.330628750  1.447625974 -0.240388156 -0.647177437
 [471]  0.376145983  0.521772505 -0.126699185 -2.030427390  0.099025427
 [476] -0.195333749 -0.495489768  1.268293794  0.095690877 -0.634413168
 [481]  1.094681695  2.603918551  0.512698224 -1.057496575 -2.144709659
 [486] -0.180357553 -1.330023731 -0.907575252 -0.988294147 -1.010863457
 [491]  0.487074661  0.514447366  0.406218552 -1.587176867  0.534934271
 [496] -1.781780428  0.388993597 -1.682715057 -0.619051389  0.553439050
 [501] -1.098761917  0.111500331  1.162731962  0.798605773  0.890835935
 [506] -0.844111192  0.530751411  0.936993329 -0.969690756 -0.042262302
 [511] -0.602491761  1.516270199  0.574427201 -0.343104659 -0.440325062
 [516]  0.172440864 -1.467228400 -0.550139850 -0.793931008  1.023050968
 [521]  0.405435647 -0.512182904 -0.061038965  1.047527988  0.040141612
 [526]  0.294546545  0.162036593  1.741215381  0.897913362  0.229134781
 [531] -0.572796236  0.053548409 -1.087258809  0.322524306  0.999418632
 [536] -0.603960041  1.267021879 -1.669817876 -1.560956544  1.761249920
 [541] -0.778019076  0.137074381  1.023121656 -0.030565711 -0.217349420
 [546] -0.283275703  0.865255902  1.099008058  0.661011124 -0.550952903
 [551]  1.142200634 -1.317174434 -1.366201374 -0.406916494  1.303918620
 [556]  1.900430544  2.201329691 -1.654142448  0.091884538  0.209229071
 [561]  1.287184625 -0.640919463 -0.698704548  0.388548211  0.011078692
 [566]  0.758319882  1.455832044 -1.069193338 -0.898702103  0.056740973
 [571]  0.436776737  0.403570046  0.205851048  0.700091030 -0.214683321
 [576]  0.021524722 -1.553291546 -0.002504039 -0.012356720  0.029406669
 [581] -0.705668012 -0.293316515 -0.134726600 -1.671895682 -0.018736589
 [586]  0.579667187  0.525915851 -1.074295795 -0.351573459  1.182243730
 [591] -0.338609505  1.384120589 -0.729217982 -0.053348427  0.054754302
 [596] -0.600125387  1.452029653  1.387906726  0.926870722  1.574690989
 [601] -0.613035535 -0.413677288 -0.207861819 -0.262533276 -1.120620845
 [606]  2.021408240  1.013876515  0.620524502 -0.582971794  0.248583087
 [611] -0.268015558 -3.117079508 -1.035326361  0.427435371  1.115661214
 [616]  0.725369949  0.080916910  1.665586589 -0.578361158  0.389117608
 [621] -2.231416717 -0.893974571 -0.051966500 -0.532492606 -0.088868940
 [626] -0.117552239 -1.035173272 -0.177817803 -1.016209892 -0.113643939
 [631] -0.261290155 -1.585419594 -0.594707685  0.897951579  0.045646981
 [636]  0.034130831  0.398890794 -0.465694175  0.167489194 -0.932887619
 [641]  0.204142087  0.195381468 -0.696315867  1.010706512  0.419505940
 [646]  0.346794791  0.489647615  1.867004915  1.137887145  1.255163288
 [651] -2.265902384 -0.561246620 -1.841409451 -0.422765894  2.678526501
 [656]  0.066319002 -0.977096046 -2.147945718  0.946856790  0.375562027
 [661] -2.290296890 -0.889474775 -0.400892210 -1.261953976  0.201467478
 [666]  0.068580322  1.467582599 -1.153102996  0.331033721  0.004519154
 [671]  0.820561339 -1.177934997 -0.205295903  2.447082596 -1.247293441
 [676]  0.036160484  0.315781241  0.762655264  1.138519540 -0.570730931
 [681]  0.399934987  0.397524287 -1.090826879  2.596569708  1.961142045
 [686] -1.519997248  0.581669152 -1.485613965  0.567520087 -1.253170816
 [691] -1.283641225 -0.749056719  0.126799495  0.208717062  0.825603993
 [696] -1.195541440  1.115623820  0.071268541 -0.831968242 -0.457459555
 [701] -0.078760171 -0.042276440  1.032087677  0.013004903 -0.841952575
 [706] -1.557282131  0.199239272  1.581810034  1.077412147 -0.155775792
 [711]  0.137333756  0.202928446  1.258079741 -0.390712311 -0.206871844
 [716] -0.954618868  0.172344675 -0.649159468  0.735055876  0.921724330
 [721] -0.792516145 -0.268503582  0.469766554  1.647161750  0.328752522
 [726]  0.085916061 -2.106900076  2.444717239 -0.169708875  0.204225298
 [731]  0.955619949  0.402261750  0.765198537  1.234697568 -0.444274411
 [736]  0.154713595  2.240473985 -0.706699028  0.490084454 -0.453277999
 [741]  0.145600784  0.251147460  1.226527559 -0.317845936  0.467442487
 [746]  1.477827001 -2.696958516 -0.401492873 -0.168272272  1.581390892
 [751]  0.864980386  0.994613923  1.431361507 -1.693332885 -1.335623366
 [756]  0.186439967  0.711474829 -0.632929422 -0.540540159 -0.431531365
 [761]  0.272972822  1.318278636  0.287010965  0.824053439 -0.364696984
 [766]  1.813209509 -2.214458805  0.214733522  1.330654394 -0.799663169
 [771]  0.016382635  0.823648548 -0.964791003 -1.007720556  1.318657566
 [776]  0.827925205 -0.034021653  1.622062492 -1.108544209  0.248311196
 [781] -0.925231022  1.879482328 -0.997222954  0.886066163  0.075870706
 [786] -1.709698845 -0.441986942  0.428649856  0.379554546 -1.572779414
 [791] -0.938559020  0.285063905  0.154637897 -3.003200944 -0.316687072
 [796]  0.148774102 -1.494002606  0.382081576 -1.053462352  0.880749742
 [801]  0.415749799  0.058913464  2.196472955 -0.291496739  0.570733409
 [806] -0.352119772 -1.836717387  1.060129682 -0.365193330 -0.792253331
 [811]  0.136283626  0.904033767  0.455169767 -1.142592849  0.223940623
 [816] -0.865014647 -1.174122520 -0.390646554 -0.506777090  0.388028171
 [821]  0.018181062 -0.196784490  0.672314453 -1.077524725 -0.847635546
 [826] -0.236345399  0.894666941  0.500446844 -1.454266075  0.194442017
 [831] -0.931443804  1.776583871  0.263737983  0.414846914 -2.483850941
 [836] -0.164089111 -1.361894925 -0.498902990  1.730574096  1.015431559
 [841] -0.433704634 -0.397035761  0.418648602  0.225511459 -0.182317280
 [846] -0.411409348  0.197560041  0.413750714 -1.329225444 -0.591844787
 [851] -0.376002901 -2.054331014  0.257551015  0.370421150  0.756370203
 [856]  1.026888472 -1.458127719 -1.614319172  0.107574746 -1.891929117
 [861] -1.140299005 -0.071903620  0.602948843 -0.213835116 -2.202089927
 [866]  0.211992724  0.905095562 -0.418059838 -0.273896062  2.008935041
 [871]  0.138369677  1.312589106  0.601850041 -1.704249786 -0.933789875
 [876]  0.136730198  0.210915099  0.197044294  0.578167607 -0.398726301
 [881] -1.212689142 -0.211528562 -0.492336491 -1.182033620  0.486180197
 [886]  0.113045099 -0.641318978 -0.168537940  0.737312884  2.004349804
 [891] -0.308153556  1.333381586  0.254593269 -0.160078257  0.462344066
 [896] -0.102939717  0.611782097  0.280663617  0.980759424  0.245783871
 [901]  0.060999344 -0.740809549  0.047474350  1.045276190 -0.206815095
 [906]  0.569211560  0.190925627 -1.704364725  1.475906198  1.102601412
 [911] -1.855766476  3.389814086  1.687752786 -1.494639937 -0.023076495
 [916] -0.434081705 -0.620828507 -1.136928495 -0.444597987  0.170470889
 [921] -0.813879039  0.984114828 -0.122395217 -0.198048372 -1.385021093
 [926] -0.215842749  0.333295064 -0.963827870 -1.444747034  0.947266546
 [931] -0.353059358 -0.674934199 -0.042649731  0.075201770 -0.254821289
 [936]  1.355659864 -0.777258387 -0.184787137 -0.088122807 -1.295676759
 [941] -0.779286481 -0.627832718  0.333747105  0.465151496 -0.650787659
 [946]  0.469031225  0.554414195 -0.348321732 -0.621187515 -1.135112973
 [951]  2.371941972  0.896801047  1.166501286  1.630665571 -0.039907981
 [956] -1.891601692 -0.244834955 -0.758703938  1.040059111 -0.625257494
 [961] -0.520490960 -0.848186349  0.284742002 -1.350565170 -0.853305431
 [966]  2.042999699  0.083486874  0.487443645  2.478444039 -1.081018356
 [971]  0.764497856  0.941070820 -0.105832621  0.107170186 -0.899731033
 [976] -1.444112971 -0.592859742 -0.883454194 -2.431872189 -0.311655537
 [981] -2.467107532  0.621220409  0.247272110  0.370445223 -0.259576925
 [986]  1.168235952 -0.692744172  0.442954704  0.347180942  1.104210537
 [991]  1.079785664  1.292484444 -0.517459933  0.563027170  0.476891418
 [996]  2.320517216 -0.553240702  0.605108686  0.256030837  0.901457239

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1
  [38] 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0
  [75] 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1
 [112] 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1
 [149] 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1
 [186] 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0
 [223] 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1
 [260] 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1
 [297] 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1
 [334] 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1
 [371] 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1
 [408] 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1
 [445] 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0
 [482] 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1
 [519] 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0
 [556] 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1
 [593] 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0
 [630] 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1
 [667] 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0
 [704] 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0
 [741] 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1
 [778] 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1
 [815] 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0
 [852] 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1
 [889] 0 0 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1
 [926] 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1
 [963] 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   162.   71.0 Blue       A    
 2     2   171.   83.3 Brown      A    
 3     3   178.   76.4 Grey       B    
 4     4   170.   67.9 Brown      A    
 5     5   170.   79.8 Blue       A    
 6     6   167.   85.4 Grey       A    
 7     7   174.   67.1 Grey       B    
 8     8   170.   79.1 Blue       A    
 9     9   175.   85.4 Green      A    
10    10   165.   76.2 Grey       A    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups